战略游戏【HYSBZ - 5329】【广义圆方树+虚树】

题目链接

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    只要在摧毁这个城市之后能够找到某两个小C占领的城市u和v，使得从u出发沿着道路无论如何都不能走到v，那么小Q就能赢下这一局游戏。

  所以，我们只需要知道有多少个点是可以作为割点的，那么求割点，并且总的点集还很少，所以就用广义圆方树加上虚树来完成了。

  广义圆方树主要就是求点双连通分量，其中，所有的圆点就是可以作为割点的，所以，统计生成虚树上有多少个可以作为割点的点，然后减去已经占领的Ki个点，就是答案了。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
//#include <unordered_map>
//#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f3f3f3f3f
#define eps 1e-8
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
#define MP(a, b) make_pair(a, b)
#define MAX_3(a, b, c) max(a, max(b, c))
#define Rabc(x) x > 0 ? x : -x
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 2e5 + 7, maxM = 4e5 + 7;
int N, M, Q;
struct Graph
{
    int head[maxN], cnt;
    struct Eddge
    {
        int nex, to;
        Eddge(int a=-1, int b=0):nex(a), to(b) {}
    }edge[maxM];
    inline void addEddge(int u, int v)
    {
        edge[cnt] = Eddge(head[u], v);
        head[u] = cnt++;
    }
    inline void _add(int u, int v) { addEddge(u, v); addEddge(v, u); }
    void clear()
    {
        cnt = 0;
        for(int i=1; i<=N; i++) head[i] = -1;
    }
} Old, Now;
int dfn[maxN], tot, low[maxN], Stap[maxN], Stop, Bcnt;
void Tarjan(int u, int fa)
{
    dfn[u] = low[u] = ++tot;
    Stap[++Stop] = u;
    for(int i=Old.head[u], v, p; ~i; i=Old.edge[i].nex)
    {
        v = Old.edge[i].to;
        if(v == fa) continue;
        if(!dfn[v])
        {
            Tarjan(v, u);
            if(low[v] >= dfn[u])
            {
                Bcnt++; Now.head[N + Bcnt] = -1;
                do
                {
                    p = Stap[Stop--];
                    Now._add(p, N + Bcnt);
                } while(p ^ v);
                Now._add(u, N + Bcnt);
            }
            low[u] = min(low[u], low[v]);
        }
        else low[u] = min(low[u], dfn[v]);
    }
}
int deep[maxN], root[maxN][20], LOG_2[maxN], dis[maxN], dfid[maxN], _id;
bool used[maxN] = {false};
void dfs(int u, int fa)
{
    root[u][0] = fa; deep[u] = deep[fa] + 1; dis[u] = dis[fa] + (u <= N ? 1 : 0); dfid[u] = ++_id;
    for(int i=0; 1 << (i + 1) < N + Bcnt; i++) root[u][i + 1] = root[root[u][i]][i];
    for(int i=Now.head[u], v; ~i; i=Now.edge[i].nex)
    {
        v = Now.edge[i].to;
        if(v == fa) continue;
        dfs(v, u);
    }
}
inline int _LCA(int u, int v)
{
    if(deep[u] < deep[v]) swap(u, v);
    int det = deep[u] -  deep[v];
    for(int i=LOG_2[det]; i>=0; i--)
    {
        if((det >> i) & 1) u = root[u][i];
    }
    if(u == v) return u;
    for(int i=LOG_2[deep[u]]; i>=0; i--)
    {
        if(root[u][i] ^ root[v][i])
        {
            u = root[u][i];
            v = root[v][i];
        }
    }
    return root[u][0];
}
int Stk[maxN], top, ans, qid[maxN];
inline bool cmp(int e1, int e2) { return dfid[e1] < dfid[e2]; }
inline void Insert(int u)
{
    if(!top) { Stk[++top] = u; return; }
    if(u == Stk[top]) return;
    int lca = _LCA(u, Stk[top]);
    if(lca == Stk[top]) { Stk[++top] = u; return; }
    while(top > 1 && dfid[lca] <= dfid[Stk[top - 1]])
    {
        ans += dis[Stk[top]] - dis[Stk[top - 1]];
        top--;
    }
    if(lca ^ Stk[top])
    {
        ans += dis[Stk[top]] - dis[lca];
        Stk[top] = lca;
    }
    Stk[++top] = u;
}
inline void init()
{
    Old.clear(); Now.clear();
    tot = Stop = Bcnt = _id = top = 0;
    for(int i=1; i<=N; i++) dfn[i] = 0;
    for(int i = 1, j = 2, k = 0; i <= (N << 1); i++)
    {
        if(i == j) { j <<= 1; k++; }
        LOG_2[i] = k;
    }
}
int main()
{
    int T; scanf("%d", &T);
    while(T--)
    {
        scanf("%d%d", &N, &M);
        init();
        for(int i=1, u, v; i<=M; i++)
        {
            scanf("%d%d", &u, &v);
            Old._add(u, v);
        }
        Tarjan(1, 0);
        dfs(1, 0);
        scanf("%d", &Q);
        int ki;
        while(Q--)
        {
            scanf("%d", &ki);
            for(int i=1; i<=ki; i++) { scanf("%d", &qid[i]); used[qid[i]] = true; }
            sort(qid + 1, qid + ki + 1, cmp);
            ans = 0; top = 0;
            for(int i=1; i<=ki; i++) Insert(qid[i]);
            while(top > 1)
            {
                ans += dis[Stk[top]] - dis[Stk[top - 1]];
                top--;
            }
            if(Stk[1] <= N) ans++;
            printf("%d\n", ans - ki);
            for(int i=1; i<=ki; i++) used[qid[i]] = false;
        }
    }
    return 0;
}